Question

The following data represent the​ high-temperature distribution for a summer month in a city for some of the last 130 years. Treat the data as a population.

Temperature ​50-59 ​ 60-69 ​ 70-79 ​ 80-89 ​90-99 ​ 100-109

Days 1 305 1469 1523 571 6

a.) Approximate the mean and standard deviation for temperature.

Mean =

Standard Deviation =

b.) Use the frequency histogram of the data to verify that the distribution is bell shaped.

- Yes, the frequency histogram of the data is bell shaped.

- No, the frequency histogram of the data is not bell shaped.

c.) According to the empirical rule, 95% of days in the month will be between what two temperatures?

____ and _____ (Round to one decimal place as needed. Use ascending order)

Answer 1

Temperature	mid point	Days	Xf	(X-xbar)2	(x-xbar)2 f
50-59	54.5	1	54.5	682.7769	682.7769
60-69	64.5	305	19672.5	260.1769	79353.95
70-79	74.5	1469	109440.5	37.5769	55200.47
80-89	84.5	1523	128693.5	14.9769	22809.82
90-99	94.5	571	53959.5	192.3769	109847.2
100-109	104.5	6	627	569.7769	3418.661
Total		3875	312447.5		271312.9

a)

Approximate the mean and standard deviation for temperature.

Mean ;

= 312447.5 / 3875

= 80.63

Standard Deviation ,

  

= 8.368

b)

ans) Yes, the frequency histogram of the data is bell shaped.

c) According to the empirical rule, 95% of days in the month will be between ,

  

= 63.89 and 97.37

****If you have any queries or doubts please comment below, if you're satisfied please give a like. Thank you!